Find the measure of the hypotenuse of a 30-60-90 triangle...?

Question

...whose longer leg has a measure of 6 meters. Give answer in simplified radical form.

Answer 1

sin 60 = 6/hypotenuse

hypotenuse = 4 sq. rt. 3

Answer 2

The longer leg will be opposite the 60 degree angle.

The sine of 60 degrees is SQRT(3)/2

The sine is equal to the opposite side over the hypotenuse.

This makes the sine = 6/hypotenuse

Equate these two:

SQRT(3)/2 = 6/hypotenuse

hypotenuse = 12/SQRT(3) = 4SQRT(3)

Answer 3

I hope this helps

http://img206.imageshack.us/img206/7738/...

Answer 4

OK - in a 30-60-90 triangle, the sides are in the proportion of 1,sqrt 3 and hypotenuse is 2.

Since the long side is 6 we have the following:

6/sqrt3 = x/1

6 = sqrt3 x

6/sqrt 3 = x

2*(sqrt3) = x . where x is the shorter side.

Double the shorter side to get the hypotenuse.

Hypotenuse = 4(sqrt 3)